Chapter 11: Flow through an embankment [ULT]
11.6 Results
Figure 158: The flow function for the slow case 12. Click OK to close the Flow functions window.
11.5.4 Execute the calculation
To select points to be considered in curves:
1. In the Staged construction mode click the Select point for curves button in the side toolbar.
The Connectivity plot is displayed in the Output program.
2. In the Select points window select nodes located nearest to (0 3) and (8 2.5) to be considered in curves.
3. Click Update to close the output program.
4. Click the Calculate button to calculate the project.
5. Save the project after the calculation has finished.
1. Click the menu Stresses > Pore pressures > Groundwater head.
2. Select the menu File > Create animation. The corresponding window pops up.
3. Define the name of the animation file and the location where it will be stored. By default the program names it according to the project and stores it in the project folder. In the same way animations can be created to compare the development of pore pressures or flow field.
4. Deselect the Initial phase and Phase 2, such that only Phase 1 is included in the animations and rename the animation accordingly. The Create animation window is shown in Figure 159 (on page 184):
Figure 159: Create animation window To view the results in a cross section:
1. Click the Cross section button in the side toolbar.
The Cross section points window pops up and the start and the end points of the cross section can be defined.
Draw a cross section through the points (2.0 3.0) and (20.0 1.0). The results in the cross section are displayed in a new window.
2. In the Cross section view select the menu Stresses > Pore pressures > p active.
3. Click the Tools menu and select the Cross section curves option . After the curves window pops up, select the menu Selection style > Individual steps.
4. Select Phase 1. The variation of the results in the cross section is displayed in a new window as shown in
Flow through an embankment [ULT]
Results
5. Do the same for Phase 2. This may take about 30 seconds which is shown in Figure 161 (on page 185).
6. The variation of the results due to different time intervals in harmonic variation at a specific cross section can be compared, see the figures below.
It can be seen that the slower variation of the external water level has a more significant influence on the pore pressures in the embankment and over a larger distance.
Figure 160: Active pore pressure variation in the cross section in Phase 1
Figure 161: Active pore pressure variation in the cross section in Phase 2
Flow through an embankment [ULT]
Results
Potato field moisture content [ULT] 12
This tutorial demonstrates the applicability of PLAXIS 2D to agricultural problems. The potato field tutorial involves a loam layer on top of a sandy base. The water level in the ditches remains unchanged. The precipitation and evaporation may vary on a daily basis due to weather conditions. The calculation aims to predict the
variation of the water content in the loam layer in time as a result of time-dependent boundary conditions.
Objectives
• Defining precipitation Geometry
Due to the symmetry of the problem, it is sufficient to simulate a strip with a width of 15.0 m, as indicated in Figure 162 (on page 186). The thickness of the loam layer is 2.0 m and the sand layer is 3.0 m deep.
Loam
Sand
Precipitation
15m 15m
0.75m 0.50m 0.75m
1.25m 0.75m Precipitation
Figure 162: Potato field geometry
12.1 Create new project
To create a new project, follow these steps:
2. In the Project tabsheet of the Project properties window, enter an appropriate title.
3. In the Model tabsheet keep the default options for Model (Plane strain), and Elements (15-Node).
4. Set the model dimensions to: xmin = 0 m, xmax = 15 m, ymin = 0 m and ymax = 5 m.
5. Keep the default values for units, constants and the general parameters and press OK.
The Project properties window closes.
12.2 Define the soil stratigraphy
Due to the geometry of the model, the options for snapping should be changed.
1. Click the Snapping options button in the bottom toolbar and snapping window appears as shown in Figure 163 (on page 187).
Figure 163: Modification of the Number of snap intervals
2. In the appearing window set the Number of snap intervals to 100.
3. Click OK to close the Snapping window.
To define the soil stratigraphy:
4. Click the Create borehole button and create two boreholes located at x = 0.75 and x = 2 respectively.
5. In the Modify soil layers window add two soil layers.
6. In the first borehole set Top = 3.75 and Bottom = 3 for the uppermost soil layer. Set Bottom = 0 for the lowest soil layer.
7. In the second borehole set Top = 5 and Bottom = 3 for the uppermost soil layer. Set Bottom = 0 for the lowest soil layer.
8. For both boreholes the Head is located at y = 4.25.
Figure 164 (on page 188) shows the soil stratigraphy defined in the Modify soil layers window.
Potato field moisture content [ULT]
Define the soil stratigraphy
Figure 164: Soil stratigraphy in the Modify soil layers window
12.3 Create and assign material data sets
Two material data sets need to be created for the soil layers.
The layers have the following properties:
Table 28: Material properties of the material
Parameter Name Loam Sand Unit
General
Soil model Model Linear elastic Linear elastic -
Drainage type Type Drained Drained -
Unsaturated unit weight γunsat 19 20 kN/m3
Potato field moisture content [ULT]
Create and assign material data sets
Parameter Name Loam Sand Unit General
Saturated unit weight γsat 19 20 kN/m3
Mechanical
Stiffness E' ref 1·103 10·103 kN/m2
Poisson's ratio ν 0.3 0.3 -
Groundwater
Classification type Type Staring Staring -
SWCC fitting method - Van Genuchten Van Genuchten -
Subsoil/Topsoil - Topsoil Subsoil -
Soil class - Clayey loam
(B9) Loamy sand
(O2) -
Flow parameters - Use defaults - From data set From data set -
Permeability in horizontal direction kx 0.01538 0.1270 m/day
Permeability in vertical direction ky 0.01538 0.1270 m/day
To create the material sets, follow these steps:
1. Create the material data sets according to Table 28 (on page 188).
2. Assign the material data set to the corresponding clusters in the model.
12.4 Generate the mesh
1. Proceed to the Mesh mode.
2. Multi-select the line segments composing the upper boundary of the model as shown in Figure 165 (on page 190).
Potato field moisture content [ULT]
Generate the mesh
Figure 165: The upper boundary of the model 3. In the Selection explorer set the Coarseness factor parameter to 0.5.
4. Click the Generate mesh button to generate the mesh. Use the default option for the Element distribution parameter (Medium).
5. Click the View mesh button to view the mesh which is shown in Figure 166 (on page 190).
Figure 166: The generated mesh 6. Click the Close tab to close the Output program.
12.5 Define and perform the calculation
The calculation process consists of two phases. In the initial phase, the groundwater flow in steady state is calculated. In Phase 1, the transient groundwater flow is calculated.
Potato field moisture content [ULT]
Define and perform the calculation
12.5.1 Initial phase
1. Proceed to the Staged construction mode . In this project only groundwater flow analysis will be performed.
2. In the Phases window select the Flow only option as the Calculation type in the General subtree.
3. The default values of the remaining parameters are valid for this phase. Click OK to close the Phases window.
4. Right-click the bottom boundary of the model and select the Activate option in the appearing menu.
5. In the Selection explorer select the Head option in the Behaviour drop-down menu and set href to 3.0 as shown in Figure 167 (on page 191).
Figure 167: Initial phase with ground water flow base 6. In the Model explorer expand the Model conditions subtree.
7. Expand the GroundwaterFlow subtree. Set BoundaryXMin and BoundaryXMax to Closed.
8. Expand the Water subtree. The borehole water level is assigned to GlobalWaterLevel.
Note: Note that the conditions explicitly assigned to groundwater flow boundaries are taken into account. In this tutorial the specified Head will be considered for the bottom boundary of the model, NOT the Closed condition specified in the GroundwaterFlow subtree under the Model conditions.
12.5.2 Transient phase
In the transient phase the time-dependent variation of precipitation is defined.
A discharge function with the following precipitation data will be defined as shown in Table 29 (on page 191).
Table 29: Precipitation data
ID Time [days] Δ Discharge [m3/day/m]
1 0 0
2 1 0.01
3 2 0.03
Potato field moisture content [ULT]
Define and perform the calculation
ID Time [days] Δ Discharge [m3/day/m]
4 3 0
5 4 -0.02
6 5 0
7 6 0.01
8 7 0.01
9 8 0
10 9 -0.02
11 10 -0.02
12 11 -0.02
13 12 -0.01
14 13 -0.01
15 14 0
16 15 0
1. Click the Add phase button to create a new phase.
2. In General subtree of the Phases window select the Transient groundwater flow as Pore pressure calculation type.
3. Set the Time interval to 15 days.
4. In the Numerical control parameters subtree set the Max number of steps stored to 250. The default values of the remaining parameters will be used.
5. Click OK to close the Phases window.
6. To define the precipitation data a discharge function should be defined. In the Model explorer expand the Attributes library subtree.
7. Right-click on Flow functions and select the Edit option in the appearing menu. The Flow functions window pops up.
8. In the Discharge functions tabsheet add a new function.
9. Specify a name for the function and select the Table option in the Signal drop-down menu.
10. Click the Add row button to introduce a new row in the table. Complete the data using the values given in Table 29 (on page 191).
Figure 168 (on page 193) shows the defined function for precipitation.
Potato field moisture content [ULT]
Define and perform the calculation
Figure 168: The Flow function window displaying the precipitation data and plot 11. Close the windows by clicking OK.
12. In the Model explorer expand the Precipitation subtree under Model conditions and activate it. The default values for discharge (q) and condition parameters (ψmin = -1.0 m and ψmax = 0.1m) are valid.
13. For the precipitation select the Time dependent option in the corresponding drop-down menu and assign the defined function.
14. In the Model explorer set DischargeFunction_1 under Discharge function as shown in Figure 169 (on page 194).
Potato field moisture content [ULT]
Define and perform the calculation
Figure 169: Precipitation in the Model explorer Note: Negative values of precipitation indicate evaporation.
12.5.3 Execute the calculation
1. Click the Calculate button , ignore the feedback and continue to calculate the project. . 2. Save the project after the calculation has finished.
12.6 Results
The calculation was focused on the time-dependent saturation of the potato field.
To view the results:
1. Click the menu Stresses > Groundwater flow > Saturation.
2. Double click the legend.
The Legend settings window pops up. Define the settings as shown in Figure 170 (on page 195).
Potato field moisture content [ULT]
Results
Figure 170: Value for settings
3. Figure 171 (on page 195) shows the spatial distribution of the saturation for the last time step.
Figure 171: Saturation field at day 15
4. Create an animation of the transient phase for a better visualisation of the results.
5. It is also interesting to create a vertical cross section at x = 4 m and draw cross section curves for pore pressure and saturation.
Potato field moisture content [ULT]
Results
Stability of dam under rapid drawdown [ULT] 13
This example concerns the stability of a reservoir dam under conditions of drawdown. Fast reduction of the reservoir level may lead to instability of the dam due to high pore water pressures that remain inside the dam.
To analyse such a situation using the finite element method, a fully coupled flow-deformation analysis is required. Time-dependent pore pressure is coupled with deformations development and used in a stability analysis. This example demonstrates how coupled analysis and stability analysis can interactively be performed in PLAXIS 2D.
Objectives
• Defining time-dependent hydraulic conditions (Flow functions).
• Defining transient flow conditions using water levels.
Geometry
The dam to be considered is 30m high and the width is 172.5m at the base and 5m at the top. The dam consists of a clay core with a well graded fill at both sides. The normal water level behind the dam is 25m high. A situation is considered where the water level drops 20m. The normal phreatic level at the right hand side of the dam is 10m below ground surface. The geometry of the dam is shown in Figure 172 (on page 196).
77.5 m 37.5 m
30 m
30 m 25 m
Fill Fill
Core
20 m
50 m 90 m
120 m 120 m
5 m
y x 5 m
Subsoil
Figure 172: Geometry of the project
13.1 Create new project
To create the new project, follow these steps:
1. Start the Input program and select Start a new project from the Quick start dialog box.
3. Keep the default units and constants and set the model Contour to xmin = -130 m, xmax = 130 m, ymin = -30 m and ymax = 30 m.
13.2 Define the soil stratigraphy
In order to define the underlying foundation soil, a borehole needs to be added and material properties must be assigned. A layer of 30 m overconsolidated silty sand is considered as sub-soil in the model.
1. Click the Create borehole button and create a borehole at x = 0.
The Modify soil layers window pops up.
2. Add a soil layer extending from ground surface (y = 0) to a depth of 30 m (y = -30).
13.3 Create and assign material data sets
Three material data sets need to be created for the soil layers.
The layers have the following properties as shown in Table 30 (on page 197):
Table 30: Material properties of the dam and subsoil
Parameter Name Core Fill Subsoil Unit
General
Soil model Model Mohr-
Coulomb Mohr-
Coulomb Mohr-
Coulomb -
Drainage type Type Undrained (B) Drained Drained -
Unsaturated unit weight γunsat 16 16 17 kN/m3
Saturated unit weight γsat 18 20 21 kN/m3
Mechanical
Young's modulus E' ref 1.5·103 20·103 50·103 kN/m2
Poisson's ratio ν 0.35 0.33 0.3 -
Cohesion c'ref - 5 1 kN/m2
Young's modulus increment E'inc 300 - - kN/m2/
m
Undrained shear strength su,ref 5 - - kN/m2
Stability of dam under rapid drawdown [ULT]
Define the soil stratigraphy
Mechanical
Friction angle φ' - 31 35 °
Dilatancy angle ψ - 1 5 °
Undrained shear strength increment su,inc 3.0 - - kN/m3
Reference level yref 30 - - m
Groundwater
Classification type - Hypres Hypres Hypres -
SWCC fitting method - Van
Genuchten Van
Genuchten Van
Genuchten -
Subsoil /Topsoil - Subsoil Subsoil Subsoil -
Soil class(standard) - Very fine Coarse Coarse -
Flow parameters - Use defaults None None None -
Horizontal permeability kx 0.1·10-3 1.00 0.01 m/day
Vertical permeability ky 0.1·10-3 1.00 0.01 m/day
To create the material sets, follow these steps:
1. Open the Material sets window.
2. Create data sets under the Soil and interfaces set type according to the information given in Table 30 (on page 197). Note that the Thermal, Interfaces and Initial tabsheets are not relevant (no thermal properties, no interfaces or K0 procedure are used).
3. Assign the Subsoil material dataset to the soil layer in the borehole.
13.4 Define the dam
The dam will be defined in the Structures mode.
In order to draw the dam with the mouse it is necessary to decrease the snap-to-grid distance. By default this distance is 1 m, but in this tutorial it should be 0.5m. In order to change the snap-to-grid distance, select the Snapping options button below the drawing area. The Spacing defines the distance between 2 grid points and the Intervals defines the amount of snap-to-grid intervals between 2 grid points. In order to have a snap-to- grid distance of 0.5m we can set either the Spacing to 0.5m and leave the Intervals to 1, or we can leave the Spacing at 1 m and set the amount of Intervals to 2.
Stability of dam under rapid drawdown [ULT]
Define the dam
1. Click the Polygon button to define a polygon through the points located at (-80 0), (92.5 0), (2.5 30) and (-2.5 30).
2. Click the Cut polygon button to create the sub-clusters in the dam. Define two cutting lines from (-10 0) to (-2.5 30) and from (10 0) to (2.5 30).
3. Assign the corresponding material datasets to the soil clusters.
13.5 Generate the mesh
1. Proceed to the Mesh mode .
2. Click the Generate mesh button in the side toolbar. For the Element distribution parameter, use the option Fine.
3. Click the View mesh button to view the mesh which is shown in Figure 173 (on page 199).
Figure 173: The generated mesh 4. Click the Close tab to close the Output program.
13.6 Define and perform the calculation
The following cases will be considered:
• A long term situation with water level at 25m.
• A quick drop of the water level from 25 to 5m.
• A slow drop of the water from 25 to 5m.
• A long term situation with water level at 5m.
In addition to Initial phase, the calculation consists of eight phases. In the initial phase, initial stresses and initial pore water pressures of the dam under normal working conditions are calculated using Gravity loading.
For this situation the water pressure distribution is calculated using a steady-state groundwater flow calculation. The first and second phases both start from the initial phase (i.e. a dam with a reservoir level at 25m) and the water level is lowered to 5 m. A distinction is made in the time interval at which this is done (i.e.
different speeds of water level reduction; rapid drawdown and slow drawdown). In both cases the water pressure distribution is calculated using a fully coupled flow-deformation analysis. The third calculation phase also starts from the initial phase and considers the long-term behaviour of the dam at the low reservoir level of 5 m, which involves a steady-state groundwater flow calculation to calculate the water pressure distribution.
Stability of dam under rapid drawdown [ULT]
Generate the mesh